Dean of the physics department at the University of Pennsylvania in 2004, after running the numbers myself and finding out that the statistical error resulting from uncorrected relativistic effects was actually an order of magnitude smaller than was suggested in the textbook (it worked out to ten meters, NOT ten kilometers, and my professor couldn't figure out what I'd done wrong so we went to the dean on sort of a bar bet). His reply was exactly this: GPS satellites do not really account for relativistic effects because they don't have to: their onboard clocks re-synch periodically through ground stations to keep them coordinated with both the Earth clocks and one another. Meaning that, to the extent relativistic effects are relevant at all, the satellite's onboard clocks are updated via ground stations anyway and regular compensation is not necessary or indeed even implemented.

He expressed to me his belief that the idea that GPS satellites accounted for relativistic effects actually originated from physics textbooks that used the GPS satellites as real-world scenario for relativistic calculations and that the eventual graduates of those classes went on to write articles about GPS satellites accounting for relativistic effects without actually knowing whether or not this was the case.

YellowSubmarine wrote:

Without relativity, GPS positions would be 65 ns off in only 2 minutes

Which might be a problem except that most GPS receivers are only accurate to at most about 100ns -- some up to a microsecond -- which in your interpretation would mean an error of not less than 100 meters. Either my math is off (a distinct possibility) or an error of 65ns would add up to pseudorange of between 20 and 70 centimeters, which becomes considerably less if the receiver is using more than three satellites.

GPS satellites re-synch their atomic clocks via ground stations multiple times a day -- I had heard every ten to 20 minutes, but can't find a source for this now. Either way, they apparently do this more often than they upgrade their ephemeris data, which I know for a fact is done every two hours.

Urban legend indeed.

Well, really a scientific legend. It's similar to some of the weird and exotic things scientists claim about human beings exposed to the vacuum of space. Actually, it seems to be the case that ALOT of what scientists understand about "Things that happen in space" contains a lot more speculation than fact and not everyone is careful to separate the two.